What is Derivative of Sin Inverse x?

The derivative of sin inverse x is 1/√(1-x²). It implies that the rate of change of the function, f(x) = sin^-1x with respect to the input variable, i.e. x, is 1/√(1-x²). Also, the slope of the curve represented by y = sin^-1x at any point x is given by dy/dx{Sin^-1x} = 1/√(1-x²). Thus, the formula for the derivative of sin inverse x can be written as follows:

Derivative of Sin Inverse x Formula

Formula for derivative of sin inverse x is given below:

(d/dx) [sin^-1x] = 1/√(1-x²)

or

(sin^-1x)’ = 1/√(1-x²)

It can be derived using the first principle of differentiation and implicit differentiation discussed as follows.

Derivative of sin inverse x is 1/√(1-x²). The derivative of any function gives the rate of change of the functional value with respect to the input variable. Sin inverse x is one of the inverse trigonometric functions. It is also represented as sin^-1x. There are inverse trigonometric functions corresponding to each trigonometric function. The derivative of a function also helps in finding the slope of the tangent to the curve represented by the function at any point.

In this article, we will learn about the derivative of sin inverse x, methods to find it including the first principle of differentiation and implicit differentiation, solved examples, and practice problems.